Papers by Keyword: Linear Vibration

Abstract: The aim of the present work is to study the linear free symmetric vibration of three-layer sandwich beam using the energy method. The zigzag model is used to describe the displacement field. The theoretical model is based on the top and bottom layers behave as Euler-Bernoulli beams while the core layer as a Timoshenko beam. Based on Hamilton’s principle, the governing equation of motion sandwich beam is obtained in order to calculate the linear frequency parameters. Two types of boundary conditions simple supported-simple-supported (SS-SS) and clamped-clamped (C-C) under the influence of materials properties and geometrical parameters are studied. The validation of results is done by comparing with another studies, which available in the literature and found good agreement between the studies.

Abstract: The aim of this paper is to examine the natural frequencies of beams for different flexural stiffness, internal simple support locations and axial moving speed. In the present investigation, the linear transverse vibrations of an axially translating beam are considered based on Euler-Bernoulli model. The beam is passing through two frictionless guides and has an internal simple support between the guides. The governing differential equations of motion are derived using Hamiltons Principle for two regions of the beam. The method of multiple scales is employed to obtain approximate analytical solution. Some numerical calculations are conducted to present the effects of flexural rigidity, mean translating speed and different internal support locations on natural frequencies.

Abstract: According to the linear vibration theory and the Lagrange Equation, this paper makes an analysis of dynamics and establishes the dynamics equation of linear vibrating screen machine system and then confirms the relationship among its vibration mass, the supporting spring stiffness , the mass of eccentric block and vibration circular frequency, it provides conditions for the precise design of the linear vibration screening machine’s bearing spring and the accurate calculation of the screening processing capacity,and it provides a basis for the vibrating screen machine’s force analysis and its strength calculation. By designing the supporting spring of the ZKB3675 linear vibrating screen machine, it verifies the practicality of the dynamics equation which is established in this paper.

Abstract: Transverse free dynamics of a beam-like nanostructure with axial load is investigated. The effects of a small size at nano-scale unavailable in classical mechanics are presented. Explicit solutions for natural frequency, vibration mode and transverse displacement are obtained by separation of variables and multiple scales analysis. Results by two methods are in close agreement.

Abstract: Evaluation method of nano-scale internal cracks by ultrasonic atomic force microscopy (UAFM) is proposed based on two approaches. The first one is a linear vibration analysis of the contact stiffness calculated from a finite element method analysis of a model including a subsurface gap. The second one is a nonlinear vibration analysis of a stiffening or softening spring representing the opening-and-closing behavior of the gap. These methods were verified by obtaining the resonance frequency mapping, the load dependence of the resonance frequency and the resonance spectra in UAFM on a subsurface gap in highly oriented pyrolytic graphite. As a result, it was proved that the proposed method is useful for evaluating the opening-and-closing behavior of the gap. Although the present study is focused on a nano-scale gap, this method is applicable to larger scale cracks using a larger tip and more stiff support than those used in AFM.